Question

Escreva na forma inrredutivel a fração geratriz de cada dizma periodica

a) 0,080808

b)2,3333

c)1,343434

d)0,410

Answer 1

a)

$a = 0.080808 \\ \\ 100a = 8.080808 \\ \\ 100a - a = 8.080808 - 0.080808 \\ \\ 99a = 8 \\ \\ a = \frac{8}{99}$

b)

$b = 2.3333 \\ \\ 10b = 23.3333 \\ \\ 10b - b = 23.3333 - 2.3333 \\ \\ 9b = 21 \\ \\ b = \frac{21}{9} = \frac{7}{3}$

c)

$c = 1.343434 \\ 100c = 134.343434 \\ \\ 10000c = 13434.343434 \\ \\ 10000c - 100c = 13434.343434 - 134.343434 \\ \\ 9900c = 13300 \\ \\ c = \frac{13300}{9900} \\ \\ \\ c = \frac{133}{99}$

d)

$d = 0.410410 \\ 1000d = 410.410410 \\ \\ 1000000 d = 410410.410410 \\ \\ 1000000d - 1000d = 410410.410 - 410.410 \\ \\ 999000d = 410000 \\ \\ d = \frac{410000}{999000} = \frac{410}{999}$